Predator-Prey Simulation with
First Order Implicit-Symplectic Scheme
by Fasma Diele ( and Marcus R. Garvie (



IMSP1 is a collection of MATLAB routines using the finite element / difference method for the dynamics of predator-prey interactions in 1 and 2 spatial dimension and time with the IMSP first order scheme (part of PRED_PREY_IMSP).

The MATLAB code is mostly self explanatory, with the names of variables and parameters corresponding to the symbols used in the finite element / difference methods described in the papers referenced below. Copies of the MATLAB codes are freely available via the link below.


  1. Garvie M.R. , "Finite difference schemes for reaction-diffusion equations modeling predator-prey interactions in MATLAB," Bulletin of Mathematical Biology (2007) 69:931-956
  2. Garvie M.R., Burkardt J., Morgan J. "Simple Finite Element Methods for Approximating Predator-Prey Dynamics in Two Dimensions using MATLAB," Bulletin of Mathematical Biology (2015) 77:548-578
  3. Diele, F., Garvie M.R., Trenchea, C. " Numerical analysis of a first-order in time implicit-symplectic scheme for predator-prey systems," submitted 2016

Download codes for IMSP1

Files you may copy include:

PRED_PREY_IMSP is distributed under the GNU GPL; see the License and Copyright notice for more information.

Last revised on June 19, 2016.